{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:MDZA3C47MCB24IHYGJJP2WIHZW","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"eb6c84eb7e2ab396833e9324574939d9a592e9cc39538442321f1619586a35dc","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-10-07T18:46:33Z","title_canon_sha256":"80939210d0d52f5c9e061a74e0c9b30f3c628a851a0299e4333f3d9a51594c43"},"schema_version":"1.0","source":{"id":"1310.1886","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.1886","created_at":"2026-05-18T02:20:18Z"},{"alias_kind":"arxiv_version","alias_value":"1310.1886v3","created_at":"2026-05-18T02:20:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.1886","created_at":"2026-05-18T02:20:18Z"},{"alias_kind":"pith_short_12","alias_value":"MDZA3C47MCB2","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"MDZA3C47MCB24IHY","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"MDZA3C47","created_at":"2026-05-18T12:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:603ada2d803344bb109f0c6a15ad5e1cd52303120e257ece7f96abaf0831f228","target":"graph","created_at":"2026-05-18T02:20:18Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We prove that a real lattice symmetric reflection positive translation invariant pure state of $\\clb=\\otimes_{\\IZ}M_d(\\IC)$ is a split state if its two points spatial correlations functions decay exponentially.","authors_text":"Anilesh Mohari","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-10-07T18:46:33Z","title":"Translation invariant pure state on $\\clb=\\otimes_{\\IZ}M_d(\\IC)$ and its split property"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.1886","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:ff38c411c04dc04587dd3dd403e4d3258f7425d989a199d00a21ce6d6e3d1cff","target":"record","created_at":"2026-05-18T02:20:18Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"eb6c84eb7e2ab396833e9324574939d9a592e9cc39538442321f1619586a35dc","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-10-07T18:46:33Z","title_canon_sha256":"80939210d0d52f5c9e061a74e0c9b30f3c628a851a0299e4333f3d9a51594c43"},"schema_version":"1.0","source":{"id":"1310.1886","kind":"arxiv","version":3}},"canonical_sha256":"60f20d8b9f6083ae20f83252fd5907cdb66dcdbc7975a856cf633b50dceb9a03","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"60f20d8b9f6083ae20f83252fd5907cdb66dcdbc7975a856cf633b50dceb9a03","first_computed_at":"2026-05-18T02:20:18.495108Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:20:18.495108Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sEStodP9q+dQy4JxJ14EPECf8xmMfL4FD12hIltNCJHT9xzu8SIb3c3R9UQhAINcB67RfqDJrTE8Vjrh6xqmCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:20:18.495840Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.1886","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ff38c411c04dc04587dd3dd403e4d3258f7425d989a199d00a21ce6d6e3d1cff","sha256:603ada2d803344bb109f0c6a15ad5e1cd52303120e257ece7f96abaf0831f228"],"state_sha256":"acf3ec631b7dbef3fd33cd06f7b04430b8a730760d5fa957cf6f510eb9ed3d18"}